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3. Define a linear transformation h : R3 + R3. The matrix representation of h over standard bases is given by 1 -2 1 H=
Posted: Tue May 10, 2022 6:25 am
by answerhappygod
- 3 Define A Linear Transformation H R3 R3 The Matrix Representation Of H Over Standard Bases Is Given By 1 2 1 H 1 (74.04 KiB) Viewed 21 times
3. Define a linear transformation h : R3 + R3. The matrix representation of h over standard bases is given by 1 -2 1 H= -3 2 5 -8 0 4 2 (a) [3 points] Write out the formula of h, i.e., find out the expression of h( y). ) z (b) [8 points] Determine the column space and null space of matrix H (i.e. Col(H) and Nul(H)) and the dimensions of Col(H) and Nul(H), respectively. ( ) [9 points] Given vectors V1, V2, V3 € R3. It is known that h(v1 + 2v2 + 3v3) =
. 16 6 25 h(4v1 +872 +003) 4 -12 16 Find out all possible v3 satisfying the above two equations.